Update GitHub pages workflow to include `contents: write`

[virgofx]

The peaceiris/actions-gh-pages GitHub action requires contents: write permission to successfully deploy.

This PR updates the permissions accordingly.

Testing

• [x] Tested by updating the GitHub workflow to run on this branch and confirmed the GitHub workflow successfully deployed.
• [x] Ensure reverting local PR deploy workflow

[shortcut-integration[bot]]

This pull request has been linked to Shortcut Story #257123: Update shortcut-client-js GitHub Workflows to ensure Pages Deploys.